The influence of non-newtonian oil film short journal bearings on the stability of a rigid rotor

The stability behaviour of rotors supported in plain cylindrical cavitated non-Newtonian fluid film journal bearings is investigated. Expressions for the journal force due to the fluid film are developed for the short bearing approximate solution to the modified form of Reynolds' equation. Linearised fluid film coefficients are used for the stability analysis. The results show that the dynamic fluid film coefficients for non-Newtonian lubricants are different from Newtonian coefficients and that they have a strong influence on the stability of rotor-bearing systems.     

Different Magnetic Models in the Design of Hydrodynamic Journal Bearings Lubricated with Non-Newtonian Ferrofluid

This work is concerned with theoretical study of hydrodynamic journal bearings lubricated with ferrofluids exhibiting non-Newtonian behavior. Based on the momentum and continuity equations for ferrofluid under an applied magnetic field, a modified Reynolds equation has been obtained. Assuming linear behavior for the magnetic material of the ferrofluid, the magnetic force was calculated. The Reynolds equation has been derived to be able to apply to any magnetic field distribution model. Using different magnetic field models, the equation has been solved numerically by the finite-difference technique with appropriate iterative technique and pressure distributions have been obtained. The boundary shape of the load-carrying active regions (positive-pressure regions) and cavitation regions (zero-pressure regions) could be then determined. The solution renders the bearing performance characteristics, namely: load-carrying capacity, attitude angle of the journal center, frictional force at the journal surface, friction coefficient and bearing side leakage. The results indicated that the flow-behavior index has a large effect on the bearing performance. When the bearing operates at high eccentricity ratios, the increase of flow-behavior index gives higher load capacity, lower attitude angle, higher frictional force, lower friction coefficient and higher side leakage. At low eccentricity ratios where the magnetic effects are significant, the effect of the flow-behavior index depends mainly on the magnetic field distribution model used.     

Stability analysis of rough journal bearings under TEHL with non-Newtonian lubricants

The combined effects of surface roughness and lubricants rheology on stability of a rigid rotor supported on finite journal bearing under thermal elastohydrodynamic lubrication have been investigated using the transient method. The newly derived time dependent modified Reynolds and the adiabatic energy equations were formulated using a non-Newtonian Carreau viscosity model. The simultaneous systems of modified Reynolds equation, elasticity equation, energy equation, and the rotor motion equation with initial conditions were solved numerically using multigrid multi-level method with full approximation technique. From the characteristic equation, the instability threshold is then obtained with various surface roughness parameters and the elastic modulus of the bearing liner materials. The results show that stability of the bearing system deteriorates with decreasing both the power law exponent and the elastic modulus of bearing liner material. The rough surface journal bearing with transverse pattern under TEHL regime exhibits better stability when compared with the rough surface journal bearing with longitudinal pattern.     

Stiffness and damping characteristics of finite width journal bearings with a non-newtonian film and their application to instability prediction

Starting from the most general fluid flow equation of the power law type expressing rate of shear in terms of powers of shear stress for non-Newtonian lubricants a modified form of Reynolds'equation is derived for dynamically loaded finite width journal bearings. The finite difference technique with successive over relaxation is used incorporating Reynolds' boundary conditions for pressure to obtain the pressure distribution. From the equations of fluid film forces, the values of stiffness and damping coefficients are obtained for a linearised case. The shear thinning effect of non-Newtonian lubricants at higher shear rates is shown to decrease the stiffness and damping values. Finally, the stability limit for such a bearing is obtained for different values of the nonlinear factor.     

Transient analysis of misaligned elastic tilting-pad journal bearing

For several reasons, almost all bearings operate in a misaligned condition, the present research work deals with analyzing the performance of a misaligned tilting-pad journal bearing under transient loading condition. The elastic and thermal distortions of the pad are considered and finite element analysis is used to calculate the pad’s elastic deformation. Using finite difference method, the Reynolds equation is simultaneously solved with the energy equation to calculate the pressure distribution and hence the other bearing performance characteristics. A modified fluid film thickness equation is used to take the effect of shaft misalignment and bearing elastic and thermal distortion into consideration.The results have shown that considering the thermo-elasto-hydrodynamic distortion improves the bearing performance in the case of misalignment shaft. And, at low values of shaft misalignment, the decrease in oil film thickness due to shaft misalignment is compensated by the increase in oil film thickness due to elastic and thermal distortions.     

浮环弹性变形对浮环动静压轴承润滑特性的影响

浮环轴承在高速工况下运行时,浮环表面在油膜压力作用下会发生弹性变形,影响轴承润滑性能。针对带有深浅腔的浮环动静压轴承,采用有限元法和有限差分法耦合求解油膜Reynolds方程、能量方程和温黏关系式,采用变形矩阵法求解弹性变形方程,计算浮环弹性变形分布;在浮环平衡的基础上,分析浮环变形对环速比、油膜承载力、端泄流量等润滑特性参数的影响。结果表明：浮环弹性变形分布与油膜压力分布呈现一致性,转速越高,偏心越大,变形越明显;考虑浮环弹性变形,浮环达到平衡状态时,内膜偏心率增加,环速比减小,轴承承载力与摩擦力矩均有所增加;由于浮环变形对内、外膜间隙及流动液阻的不同影响,使得内膜端泄流量增加,外膜端泄流量减少。     

弹性变形对径向轴承弹流润滑性能的影响

本文以上具有不同弹性模量、泊松系数的两种轴承材料为例分析了弹性变形对有限长径向滑动轴承的弹流润滑性能的影响。流体动力润滑方程采用雷诺方程,应用力学问题的通用有限元软件ＭＡＲＣ产生柔度矩阵计算弹性变形。对比分析了二种轴承的油膜压力分布、油膜厚度分布、最小油膜厚度以及承载能力。     

Effects of couple stresses in the cyclic squeeze films of finite partial journal bearings

Based upon the microcontinuum theory, the present paper is to theoretically study the pure squeeze-film behavior of a finite partial journal bearing with non-Newtonian couple-stress lubricants operating under a time-dependent cyclic load. To take into account the couple stress effects resulting from the lubricant blended with various additives, the modified Reynolds equation governing the film pressure is obtained from Stokes equations of motion. The film pressure is numerically solved by using the Conjugate Gradient Method. Bearing characteristics are then calculated from the nonlinear motion equation of the journal. According to the results obtained, the effects of couple stresses result in a decrease in the value of eccentricity of the journal center. The finite partial bearing with a couple stress fluid as the lubricant yields an increase in the minimum permissible clearance and provides a longer time to prevent the journal-bearing contact.     

Steady state and stability characteristics of a hydrodynamic journal bearing with a non-Newtonian lubricant

The effect of the non-Newtonian behaviour of lubricants, resulting from the addition of polymers, on the performance of hydrodynamic journal bearings was investigated. An empirical fluid flow equation which adequately represents the flow behaviour of lubricant was used to obtain a modified form of Reynolds' equation. Finite difference numerical solutions were obtained for steady state conditions at various width-to-diameter ratios. The results show a strong influence of the width-to-diameter ratio on the load capacity of journal bearings. Linearised stiffness and damping coefficients were evaluated from the fluid film force equations for the unsteady motion of the journal centre and were used to predict the stability limits of a simple rigid rotor-bearing system which showed a reduction in threshold speeds. The steady state load capacity and stability limits were verified experimentally for finite width bearings.     

Performance analysis of flexible multirecess hydrostatic journal bearing operating with micropolar lubricant

This paper presents the analytical study of the effect of the bearing shell flexibility on the performance of multirecess hydrostatic journal bearing system operating with micropolar lubricant. The modified Reynolds equation for the flow of micropolar lubricant through constant flow valve‐compensated hydrostatic journal bearing has been solved by finite element technique based on Galerkins method, and the resulting elastic deformation in the bearing shell due to fluid‐film pressure has been determined iteratively, in which the deformation coefficient accounts for the bearing shell flexibility. The computed results suggest that the influence of the micropolar effect on bearing performance characteristics is significantly affected by the bearing shell flexibility. Copyright © 2012 John Wiley & Sons, Ltd.     

Elastohydrodynamic lubrication analysis of a functionally graded layered bearing surface,with particular reference to 'cushion form bearings' for artificial knee joints

Elastohydrodynamic lubrication of a functionally graded layered (FGL) bearing surface, whose elastic modulus increases with depth from the bearing surface, was investigated in this study. The finite difference method was employed to solve the Reynolds equation, simultaneously with the elasticity equation of the bearing surface, under circular point contacts. The finite element method was adopted to solve the elasticity equation for the FGL bearing surface. The displacement coefficients thus obtained were used to calculate the elastic deformation of the bearing surface, required for the elastohydrodynamic lubrication analysis. Good agreement of the predicted film thickness and pressure distribution was obtained, between the present method and a previous study for a single layered bearing surface with a uniform elastic modulus. The general numerical methodology was then applied to an FGL bearing surface with both linear and exponential variations in elastic modulus, with particular reference to the 'cushion form bearing' for artificial knee joints. The predicted film thickness and pressure distribution were shown to be quite close to those obtained for a single layer under typical operating conditions representative of artificial knee joints, provided that the elastic modulus of the single layer was chosen to be the average elastic modulus of the graded layer.     

Numerical analysis of journal bearings lubricated with micropolar fluids including thermal and cavitating effects

A numerical study of the non-Newtonian behavior for a finite journal bearing lubricated with micropolar fluids is undertaken considering both thermal and cavitating effects. The modified Reynolds equation and energy equation are derived based on Eringen's micropolar fluid theory. The solution to the modified Reynolds equation is determined using the Elord's cavitation algorithm. The effects of the size of material characteristic length and the coupling number on the thermohydrodynamic performance of a journal bearing are investigated. It is shown, compared with Newtonian fluids, that micropolar fluids exhibit the increase in load capacity and temperature, but the decrease in coefficient of friction and side leakage flow. It is also indicated that, in the full film region, micropolar fluids increase the values of non-dimensional density, while in the cavitated region, both micropolar fluids and Newtonian fluids yield the same values of the fractional film content.     

The effect solid particle lubricant contamination on the dynamic behavior of compliant journal bearings

The proposed work concerns a theoretical and numerical investigation of the effect of solid particle contamination of lubricant oils on the static and dynamic characteristics of a finite length compliant journal bearing operating under isothermal conditions with laminar flow. In the present investigation, we use simple models based on the Einstein's mixture theory, which is characterized by the presence of suspended rigid particles in a fluid. Using the classical assumptions of lubrication, a Reynolds equation is derived and solved numerically by the finite difference method. The displacement field at the fluid film bearing liner interface due to pressure forces is determined using the elastic thin layer model. The results obtained show that the presence of suspended rigid particles in the lubricating oil (solid contamination) has significant effects on the hydrodynamic performance characteristics such as the pressure field, friction force, flow rate, elastic surface deformation as well as stability maps of the rotor‐bearing system (critical mass and whirl frequency) especially at high volumetric concentration.     

Effects of lubricant additives on the performance of hydrodynamically lubricated journal bearings

A non-Newtonian rheological model to investigate theoretically the effects of lubricant additives on the steady state performance of hydrodynamically lubricated finite journal bearings is introduced. In this model, the non-Newtonian behavior resulting from blending the lubricant with polymer additives is simulated by Stokes couple stress fluid model. The formed boundary layer at the bearing surface is described through the use of a hypothetical porous medium layer that adheres to the bearing surface. The Brinkman-extended Darcy equations are utilized to model the flow in the porous region. A stress jump boundary condition is applied at the porous media/fluid film interface. A modified form of the Reynolds equation is derived and solved numerically using a finite difference scheme. The effects of bearing geometry, and non-Newtonian behavior of the lubricant on the steady-state performance characteristics such as pressure distribution, load carrying capacity, side leakage flow, and coefficient of friction are presented and discussed. The results showed that lubricant additives significantly increase the load carrying capacity and reduce both the coefficient of friction and the side leakage as compared to the Newtonian lubricants.     

TEHD Analysis for Tilting-Pad Journal Bearings Using Upwind Finite Element Method

A general approach for incorporating heat transfer and elastic deformation effects into a tilting-pad journal bearing simulation model is presented. A global analysis method is used, which includes variable viscosity and heat transfer effects in the fluid film, elastic deformation and heat conduction effects in the pads, and elastic deformation effect in the pivots. The two-dimensional variable viscosity. Reynolds equation produces pressure distributions in the axial and circumferential directions. The energy equation is two-dimensional, assuming that the temperature variation in the axial direction is negligible. The elasticity and heat conduction models are also two-dimensional, being in the midline cross-section of the bearing, including the circumferential and cross-film directions. An upwind technique is used in the finite element formulation of the energy equation to remove numerical instability due to the convective term. Simulation results are compared with the test and predicted values of previous researchers.     

卧式水电机组用径向滑动轴承热弹流特性分析

研究轴颈挠度和瓦块表面热弹变形对卧式水电机组径向滑动轴承静态润滑性能的影响。推导考虑轴颈挠度和轴瓦热弹变形后的油膜厚度表达式;用中心差分法结合ANSYS软件联立求解雷诺方程、能量方程、固体热传导方程、密度方程、黏度方程和轴瓦热弹变形等,得到径向滑动轴承的热弹流润滑(TEHD)特性,并与不计入轴颈挠度及轴瓦热弹变形的油膜动压润滑特性进行比较。结果表明:在考虑轴颈挠度和轴瓦瓦面热弹变形的影响后,油膜压力、温度、厚度沿着轴承宽度中心线的对称特性消失;油膜压力峰值增大,峰值点位置由轴向中心区偏移至出口区;油膜温度峰值增大,最高温度发生在出口区;润滑区内的最小油膜厚度大幅度减小,油膜最小厚度处于出口侧边界附近;轴承润滑流量减小,损耗略有增大;轴承稳态运行时,轴颈偏位角基本一致。     

A Study of Dynamically Loaded Journal Bearings Lubricated with Non-Newtonian Couple Stress Fluids

This paper is to theoretically investigate the behavior of dynamically loaded journal bearings lubricated with non-Newtonian couple stress fluids. To take into account the couple stress effects due to the lubricants blended with various additives, the modified Reynolds equation for dynamic loads governing the film pressure is derived. The film pressure is solved numerically with Reynolds boundary conditions and then various bearing characteristics are calculated. The effects of couple stresses on bearing performance characteristics are analyzed. The results conclude that couple stress fluids lubrication improves the bearing performance under dynamic loads.     

弹性变形对大型球磨机轴承性能的影响

研究弹性变形对大型球磨机滑履轴承性能的影响。采用有限差分法求解简化形式的N-S方程,得出油膜压力分布和膜厚分布;借助有限元软件ANSYS分析中空轴和轴瓦的弹性变形。将变形作为油膜变化的条件,油膜压力分布作为变形的条件,进行耦合分析,得出润滑油膜厚度及压力分布。结果表明:考虑中弹性变形时计算得到的最小油膜厚度小于未考虑弹性变形时的厚度,且球磨机四块瓦的油膜厚度分布规律不同,表明中空轴和轴瓦的变形对膜厚分布规律、压力分布及最小膜厚有较大影响,设计时必须考虑弹性变形的影响,以防止出现油膜过薄导致轴承失效。     

Numerical investigation of pocketed slip slider bearing with non-Newtonian lubricant

Boundary slip as well as surface texturing is an effective method to improve the tribological performance of lubricated mechanical components. This article analyzes the combined effect of single texturing (pocketing) and wall slip on pressure that strongly related to the load-carrying capacity of slider bearing. The modified Reynolds equation for lubrication with non-Newtonian power-law fluid is proposed. The equation was solved numerically using a finite difference equation obtained by means of the micro-control volume approach. Further, numerical computations for slider bearing with several power-law indexes were compared with the presence of the pocket and slip. The numerical results showed that the characteristic of non-Newtonian is similar to Newtonian fluid with respect to hydrodynamic pressure distribution. The maximum load support is achieved when the pocket depth is equal to the film thickness.     

内燃机主轴承EHD模拟计算研究

在充分考虑轴承座、瓦背、减摩合金层的弹性变形及轴颈、轴瓦表面粗糙度因素的影响基础上,对某4100QB柴油机主轴承进行了综合的EHD模拟计算研究。采用有限差分法与有限元法相结合对轴承的油膜压力、油膜厚度、弹性变形、表面粗糙度进行了耦合分析,并将EHD耦合算法结果与刚性分析结果及仅考虑轴瓦弹性变形的分析结果进行了比较分析。结果表明,综合考虑轴承座、瓦背、减摩合金层弹性变形及轴颈、轴瓦表面粗糙度因素影响的弹流润滑研究更符合实际工况,其油膜厚度增大,油膜压力减小,油膜承载区扩大,且在轴承载荷峰值处表现最为明显。